Categorial Categories and Slice Categories

Let D1, D2, D be non empty sets and let x be an element of [: [:D1, D2 :], D :]. Then x1,1 is an element of D1. Then x1,2 is an element of D2. Let D1, D2 be non empty sets and let x be an element of [:D1, D2 :]. Then x2 is an element of D2. Next we state the proposition (1) Let C, D be category structures. Suppose the category structure of C = the category structure of D. If C is category-like, then D is categorylike. A category structure has triple-like morphisms if: (Def.1) For every morphism f of it there exists a set x such that f = 〈〈 dom f, cod f〉, x〉. One can verify that there exists a strict category has triple-like morphisms. Next we state the proposition (2) Let C be a category structure with triple-like morphisms and let f be a morphism of C. Then dom f = f1,1 and cod f = f1,2 and f = 〈〈 dom f, cod f〉, f2〉.